Magnetic and Electronic Phase Diagram and Superconductivity in the Organic Superconductors k-(BEDT-TTF)2X

The magnetic susceptibility of the organic superconductors $\kappa$-(h8 or d8-ET)$_{2}$$X$, $X =$ Cu(NCS)$_{2}$ and Cu[N(CN)$_{2}$]Br has been studied. A metallic phase below $T^{*} =$ 37 $\sim$ 38 K for $X =$ Cu[N(CN)$_{2}$]Br and 46 $\sim$ 50 K for $X =$ Cu(NCS)$_{2}$ has an anisotropic temperature dependence of the susceptibility and the charge transport. Partial charge-density-wave or charge fluctuation is expected to coexist with the metallic phase instead of the large antiferromagnetic fluctuation above $T^{*}$. The phase diagram and the superconductivity of $\kappa$-(ET)$_{2}$$X$ are discussed in connection with this phase.Comment: 5 pages, 4figures, REVTeX, references are corrected, accepted for pubication in Phys. Rev.

Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general. In this article, using the geometry of K_C orbits on the generalized flag variety G_C/P_C, we give a necessary and sufficient condition on the triple (g,k, p) such that the restriction X|_k always contains simple k-modules for any g-module $X$ lying in the parabolic BGG category O^p attached to a parabolic subalgebra p of g. Formulas are derived for the Gelfand-Kirillov dimension of any simple k-module occurring in a simple generalized Verma module of g. We then prove that the restriction X|_k is multiplicity-free for any generic g-module X \in O if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n), or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free for any symmetric pair (g, k) and any parabolic subalgebra p with abelian nilradical and for any generic g-module X \in O^p. Explicit branching laws are also presented.Comment: 31 pages, To appear in Transformation Group

Bogoliubov Theory and Lee-Huang-Yang Corrections in Spin-1 and Spin-2 Bose-Einstein Condensates in the Presence of the Quadratic Zeeman Effect

We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.Comment: v3: 62 pages, 18 figure